updated 07/07/2012 AT 4:00 PM ET
•originally published 07/07/2012 AT 7:30 PM ET
For much of the past few days, lawyers for Tom Cruise and Katie Holmes have been working behind closed doors to iron out an agreement between the two stars that would avoid a long, public divorce fight.
Cruise “doesn’t want his family dragged through the mud,” says one source. “They both love their daughter.”
One crucial issue: where Suri, 6, will live and who will raise her.
Holmes, 33, who filed for sole legal custody, would like to bring up her daughter in New York City. Cruise, 50, lives primarily in Los Angeles, although he owns properties in Manhattan.